Finite difference approximations for the fractional advection-diffusion equation

摘要

Fractional order diffusion equations are viewed as generalizations of classical diffusion equations, treating super-diffusive flow processes. In this Letter, in order to solve the two-sided fractional advection-diffusion equation, the fractional Crank-Nicholson method (FCN) is given, which is based on shifted Grunwald-Letnikov formula. It is shown that this method is unconditionally stable, consistent and convergent. The accuracy with respect to the time step is of order (Delta t)(2). A numerical example is presented to confirm the conclusions.